Introduction

This is a notebook intended to explain at large what we have done with PRSIM on the Outaouais River Watershed. First of all, let’s get an idea of the area of study.

Figure 1: Outaouais river watershed

The watershed surface is about 140 000 km2 and consists of 42 basins. On the Outaouais river watershed we can find infrastructures that are designed to withstand PMF, 1:10 000 and 1:1 000 return year floods depending on the canadian dam classification.

Our main interest in PRSIM is the fact that spatial and temporal intercorrelations are taken into account while producing the stochastic simulations.

Extreme floods at the basin level

In our first trials with PRSIM we found out that for some basins certain unrealistic peakflows where simulated. Even for extreme cases. In fact, some 1:100 year peakflows where higher than our PMF (Probable maximum flood). In order to continue to explore the generation, we limited the kappa generation function to 0.9995 right-side limit. With this modification, we found out more realistic hydrogram shapes and the statistics up to 1:100 years return peakflow was coherent with what we calculated using the observations. is this a correct procedure?

As said before, in order to explore our simulations we first calculated the marginal return periods at each basin of the Outaouais following the cunnane plotting positions and compare them to our inferences on the observed data.

The next table is our simulated peakflow during spring for return periods up to 10 000 year flood:

Bassins X10000 X2000 X1000 X200 X100 X50 X20 X10
Bark Lake 1242.3440 1162.7528 1128.3389 1027.5851 976.9681 919.7799 830.5930 749.3901
Baskatong 7508.6798 6936.3604 6652.5228 6014.5007 5730.1250 5423.0333 4957.1479 4534.6255
Cabonga 1125.7898 1036.7577 996.7076 895.6267 851.7834 803.6719 730.3051 665.4387
Carillon et Hull 3171.9298 2985.5188 2882.5554 2587.7296 2443.5886 2281.5225 2040.0728 1827.8960
Chelsea 758.9450 682.7851 652.4290 563.0907 521.3139 479.3040 419.4095 370.2393
Chenaux et Noire 3401.1229 3241.5263 3131.3853 2871.6851 2740.5065 2588.5080 2362.4206 2154.4265
Chute-des-Chats 651.7046 614.4288 590.5129 517.2233 477.2710 431.4022 364.3690 309.5378
Des Joachims 1883.3424 1776.0331 1718.2316 1569.6304 1491.7209 1405.7223 1273.2441 1155.5711
Dozois 3588.3049 3347.0108 3231.0857 2987.6620 2853.8488 2718.1679 2504.4925 2303.9860
High Falls 587.3685 547.1364 525.6787 458.6889 425.7115 385.7853 328.2235 284.8513
Kamaniskeg 1554.0059 1459.8875 1413.6170 1275.1912 1206.0303 1133.5846 1023.0774 925.9162
Kiamika 523.1573 465.8427 444.9111 395.4081 373.0870 349.3216 313.2793 282.8991
Kipawa 2652.1450 2508.3623 2462.0204 2285.5990 2197.9174 2091.7752 1923.4434 1764.1874
Lac des Quinze 3541.5347 3263.6096 3128.3798 2809.9814 2661.2444 2502.1996 2254.3587 2032.2985
Lac du poisson blanc 1362.7436 1280.2980 1236.0437 1111.6795 1050.2173 979.4608 875.9812 782.4381
Lac Temiscamingue a Angliers 4945.1286 4522.0616 4319.4792 3819.2431 3567.2301 3309.1453 2907.3624 2563.1209
Lac Victoria et lac Granet 1003.1379 921.1153 891.1498 806.4916 764.2619 720.7806 651.7582 588.1776
Lady Evelyn 652.4476 607.3596 575.3984 512.9231 483.8128 453.5861 406.9866 365.3889
Lower Notch et Indian Chute 1585.7152 1458.3929 1399.3685 1228.8869 1153.6685 1075.2847 957.3077 855.9516
Madawaska-Arnprior 488.9412 452.8840 435.3450 385.2244 359.4894 332.1919 289.3184 251.9959
Maniwaki 1847.3500 1740.9900 1700.9626 1553.1014 1479.3017 1397.7690 1271.0410 1155.8982
Masson 329.2685 300.6092 288.1108 249.3761 228.6906 206.3624 175.1910 151.0096
Mistinikon 917.2477 847.1981 805.5629 700.6506 651.1667 599.4349 523.9473 459.7918
Mitchinamecus 625.7461 576.6520 550.5979 488.8265 461.6761 430.3501 386.1759 347.2392
Mont-Laurier 2184.1479 1985.8289 1906.6715 1701.1338 1610.7372 1512.2174 1365.0921 1235.4042
Mountain Chute 580.9590 537.9949 516.7268 465.4419 436.8958 406.2368 361.5934 322.2887
Otto Holden 1038.1692 969.3162 934.2415 842.7119 796.2641 746.8982 673.3623 608.6809
Paugan 1229.7737 1149.6683 1112.5533 1013.1686 966.4136 913.0881 831.3040 757.5732
Rabbit Lake 385.3661 358.2604 341.9620 307.7900 290.6256 272.0462 243.9844 218.7826
Rapide-2 484.8034 442.4072 425.1599 377.6698 354.2666 331.0405 296.4513 265.5448
Rapide-7 1415.3769 1323.8926 1281.2016 1160.7964 1101.6318 1037.6544 938.4561 849.4832
Riviere Blanche 934.7308 871.9891 835.8835 740.6083 699.0842 654.3956 588.8455 527.6535
Riviere Bonnechere 733.2254 704.3285 686.3160 628.3024 598.2029 564.0174 511.9187 462.9664
Riviere Coulonge 2403.9427 2258.7767 2195.9117 1988.5072 1884.9845 1766.9334 1587.5934 1427.5333
Riviere Dumoine 1563.5836 1450.1066 1392.9671 1245.8827 1175.6893 1097.8666 984.0699 885.9007
Riviere Kinojevis 1361.0259 1264.3045 1209.0235 1066.5307 1003.9986 938.0917 841.0084 756.1017
Riviere Mattawa 947.1214 883.5909 856.7752 779.4886 743.2398 700.0562 632.5179 573.5357
Riviere Mississippi 1080.2434 1036.7325 1011.9443 923.6757 873.6932 821.2574 738.0254 662.5320
Riviere Petawawa 1605.9440 1526.2073 1485.9140 1365.5982 1301.2187 1229.7161 1117.8898 1015.5404
Riviere Petite Nation 662.3253 627.4568 612.1940 567.2816 546.1720 520.9882 480.7466 442.3887
Riviere Rideau 1851.7313 1708.8029 1640.3048 1458.8985 1371.4654 1274.7918 1126.7549 996.9618
Riviere Rouge 3146.4555 2928.8170 2825.7133 2579.4912 2467.0482 2343.2229 2144.9797 1964.4844
Riviere South Nation 2728.1102 2520.3766 2396.9181 2113.5804 1976.5231 1822.1965 1588.4452 1386.3621

As you can see, in some watersheds the right tail is pretty ‘flat’. See at Rapide-2. Meaning that the difference in between the extreme quantiles is not very large.

The next table is our simulated 70-day volume during spring for return periods up to 10 000 year flood:

Bassins X10000 X2000 X1000 X200 X100 X50 X20 X10 X2
Bark Lake 570.0919 550.7729 533.9670 460.5318 410.7656 361.2298 322.2216 296.48812 184.69273
Baskatong 3646.6289 3417.4927 3274.4803 2636.8589 2260.9075 2100.3213 1960.2755 1818.65280 1199.95158
Cabonga 428.6745 416.1265 409.9660 390.6933 379.0166 362.1265 330.6289 298.95303 182.49408
Carillon et Hull 1164.5721 1115.3439 1085.4031 1019.3922 980.8011 937.1003 862.5117 784.91155 480.74020
Chelsea 473.4902 459.5226 447.9296 394.7819 352.7340 298.0995 228.0733 190.70084 95.53211
Chenaux et Noire 1162.8814 1138.5408 1115.5883 1029.8530 970.6010 900.5709 823.4037 738.84514 496.09822
Chute-des-Chats 331.8182 311.9161 300.9632 250.0273 230.0187 209.3233 173.6805 138.02646 59.09129
Des Joachims 828.4144 786.9286 759.4712 681.3078 663.2487 637.4748 590.1857 533.58300 306.51743
Dozois 1271.3434 1232.0854 1192.6040 1051.2271 961.7782 882.2263 819.6346 784.72526 569.00202
High Falls 301.1274 292.2456 283.8487 258.6468 241.1290 217.0880 177.0695 139.74413 58.41111
Kamaniskeg 551.3999 532.7702 517.8461 454.4153 422.9528 397.0795 356.0548 326.69426 217.38325
Kiamika 324.6541 308.6289 293.2855 237.3662 206.3139 177.6395 162.4465 148.78484 89.90630
Kipawa 959.6839 922.4593 896.5658 773.7121 694.9050 609.7161 582.2369 554.22637 385.05625
Lac des Quinze 1762.7627 1683.8087 1614.3934 1358.8260 1295.1868 1238.1896 1139.5028 1032.88655 605.25710
Lac du poisson blanc 696.8718 685.3342 677.3659 632.9789 600.3594 563.0298 496.6441 430.53665 213.25047
Lac Temiscamingue a Angliers 2256.1413 2196.7296 2166.8774 2049.2031 1973.3278 1885.8052 1722.4812 1535.90827 818.46774
Lac Victoria et lac Granet 366.2829 359.5624 354.1509 338.7682 329.9826 317.3167 293.4375 268.91618 159.23925
Lady Evelyn 250.6022 240.1384 233.3927 219.7487 212.2004 202.3367 186.0600 169.95740 99.95993
Lower Notch et Indian Chute 716.0813 684.0630 666.6522 584.9894 538.8934 510.4881 470.9044 431.80911 253.89152
Madawaska-Arnprior 305.1468 291.0010 284.4341 263.5525 250.8762 233.4409 197.2604 159.77136 61.09901
Maniwaki 617.9192 594.0401 579.4065 512.8340 499.0270 483.4548 451.5381 413.03658 266.74202
Masson 184.6402 179.9773 175.8907 158.7582 147.0237 132.6033 106.0039 81.15489 30.52589
Mistinikon 437.7329 428.7347 422.1876 390.7859 366.2304 334.4623 281.3621 240.75707 123.03825
Mitchinamecus 289.2250 270.2562 260.7328 232.0122 219.6334 209.0825 192.6995 175.08971 101.86703
Mont-Laurier 802.8084 758.6056 731.1178 664.9939 638.3261 612.9637 563.4618 504.96572 307.77444
Mountain Chute 270.6613 262.4304 256.7766 237.3188 226.3866 216.1628 200.0959 181.07896 97.24514
Otto Holden 455.6394 435.9166 415.9481 354.7893 329.5435 306.5768 269.5283 245.07982 154.30405
Paugan 397.4899 386.4904 380.9314 356.6439 340.1350 320.9545 291.3756 267.12346 171.44453
Rabbit Lake 215.8183 206.8694 198.9388 166.5558 147.0084 134.0209 123.0762 112.22020 64.87362
Rapide-2 252.1724 237.2582 228.1820 203.2302 191.4492 180.9851 165.9085 150.29249 86.86837
Rapide-7 487.1321 480.5640 474.3391 452.6114 438.9440 421.2849 390.4551 356.73254 219.13244
Riviere Blanche 446.2360 420.5961 399.4028 328.7081 304.9224 288.0476 265.5729 243.87579 153.18499
Riviere Bonnechere 250.5985 239.7549 232.3157 216.5365 206.9859 195.0474 177.5458 158.94685 95.09106
Riviere Coulonge 1028.4278 977.0884 954.5761 878.9607 850.9815 813.9388 740.6389 654.05832 370.45614
Riviere Dumoine 652.5433 637.1263 623.0187 571.9097 536.9688 493.6087 417.6699 350.82518 194.93202
Riviere Kinojevis 768.4544 683.5832 630.9470 556.6054 530.4467 500.3071 447.4350 397.35798 239.52448
Riviere Mattawa 456.7110 434.9477 414.9948 345.3390 306.2777 281.2000 252.2116 229.13937 147.59000
Riviere Mississippi 337.0428 329.1230 322.7047 302.6802 294.2935 281.9381 257.2086 234.78225 140.63049
Riviere Petawawa 709.2614 667.1398 635.9460 534.6863 474.3391 436.7133 399.7361 370.07331 238.65845
Riviere Petite Nation 185.4273 179.7203 176.5584 167.7850 162.9259 158.0503 149.5898 140.25983 96.81653
Riviere Rideau 922.4425 888.6210 872.1046 810.7300 777.7792 741.1529 670.5979 591.88253 301.23575
Riviere Rouge 1464.8422 1395.8310 1340.4687 1150.9947 1046.5599 920.0046 820.2892 768.94513 510.81446
Riviere South Nation 2469.2298 2318.1192 2210.8473 1868.0112 1652.9964 1433.7505 1221.5425 1059.98274 581.00035

The next table is our simulated peakflow volume during summer-autumn for return periods up to 10 000 year flood:

Bassins X10000 X2000 X1000 X200 X100 X50 X20 X10 X2
Bark Lake 225.38395 210.78825 200.58190 181.74004 171.05949 159.01671 142.28235 126.66166 70.96534
Baskatong 1845.02267 1729.04453 1652.48110 1452.33643 1364.60778 1265.88806 1097.65235 948.86050 497.13023
Cabonga 309.78892 295.20757 285.33669 251.63116 233.01947 217.39342 196.54990 178.92355 107.77959
Carillon et Hull 882.38383 837.53107 806.45125 684.39493 630.50020 591.46913 516.45387 437.46054 194.61018
Chelsea 335.81747 297.01155 276.28445 210.67281 182.40332 154.94756 127.28632 106.00641 44.04528
Chenaux et Noire 641.68435 603.02883 579.74638 519.93983 487.47706 450.13341 387.51123 340.72481 225.51537
Chute-des-Chats 470.71107 458.25953 443.45040 382.56046 340.69960 290.72574 206.57766 132.90117 29.19774
Des Joachims 530.83294 517.10341 505.00314 456.37682 416.72421 361.79256 271.02197 233.04446 132.83569
Dozois 920.85722 876.05399 851.44452 759.75751 707.61855 654.23777 577.42058 512.92772 298.91545
High Falls 123.17209 114.14658 109.23322 91.13325 81.53298 73.50624 63.93674 54.71485 31.10594
Kamaniskeg 349.00949 331.46200 321.02763 285.92559 266.64139 247.04917 216.36571 185.99473 92.08904
Kiamika 125.72204 122.27351 119.39810 108.82941 101.97180 93.21011 79.17474 66.81531 33.28293
Kipawa 600.20413 589.82403 582.34062 540.55486 512.52706 472.69940 405.08380 361.01627 222.37855
Lac des Quinze 1341.99433 1241.67350 1194.85200 970.51985 873.01098 773.88262 620.97050 493.62196 224.90264
Lac du poisson blanc 264.63470 254.41239 249.67827 234.14181 223.02086 210.09415 185.45003 164.25206 92.92919
Lac Temiscamingue a Angliers 1056.85737 1004.22141 972.85259 900.73983 849.87216 787.24955 671.75004 551.92678 246.63260
Lac Victoria et lac Granet 278.22131 256.99822 246.18805 211.81569 193.08592 175.52727 150.70169 131.94271 71.61453
Lady Evelyn 132.97801 130.32496 128.63209 123.15032 118.60565 112.29181 101.18460 88.69618 44.81741
Lower Notch et Indian Chute 376.90252 362.95459 356.08719 320.08557 297.43549 270.75121 224.45447 184.83626 93.09650
Madawaska-Arnprior 101.14809 94.09446 90.37488 81.10333 75.84809 69.66174 57.30110 44.26953 22.24211
Maniwaki 420.70892 403.80015 393.83628 352.51850 325.59883 295.51583 248.94891 213.59483 118.48863
Masson 65.13289 61.19537 58.45389 48.82929 43.83309 39.40655 33.83599 28.68487 16.80749
Mistinikon 196.50841 185.74139 179.53780 158.64840 145.88162 131.23392 108.81131 93.56531 49.68093
Mitchinamecus 216.72300 196.11452 190.09162 167.11845 154.63016 140.14936 113.77080 93.20453 45.34761
Mont-Laurier 729.08758 683.06444 655.35111 554.51809 501.70602 446.17455 362.82187 295.60017 151.90628
Mountain Chute 219.54362 211.41893 202.89039 175.88361 162.49549 145.59336 118.56855 93.91681 35.91712
Otto Holden 222.98092 210.20768 205.24698 190.52163 179.89914 168.22309 147.45197 128.97026 65.65825
Paugan 310.87555 297.98526 288.25316 249.08284 230.85876 210.92887 174.92006 147.00014 78.30474
Rabbit Lake 113.42977 104.90243 99.51547 82.76410 76.43192 69.48152 58.87571 49.58254 22.55023
Rapide-2 122.66465 117.76625 115.77057 109.10584 104.46622 97.78349 84.68072 70.76665 30.47631
Rapide-7 422.81831 402.90522 387.87295 353.05270 332.64443 307.78728 264.96478 221.92664 105.12817
Riviere Blanche 248.48044 232.40169 220.57276 184.91465 165.31397 146.54781 116.61465 96.85292 49.23170
Riviere Bonnechere 203.26725 185.93845 174.08861 139.49134 124.35177 111.45909 94.19408 81.55753 44.18148
Riviere Coulonge 521.45756 505.05579 494.46282 446.08685 416.79952 380.57484 329.17176 291.14472 156.08903
Riviere Dumoine 313.77231 296.35681 285.37067 251.73852 235.07125 218.08933 192.76679 170.84516 106.49939
Riviere Kinojevis 588.67901 561.76509 538.08149 462.10885 415.54147 367.56855 282.50571 216.02874 91.65229
Riviere Mattawa 200.51960 195.16639 192.20419 176.62114 164.98038 148.63720 127.58722 111.65384 58.18963
Riviere Mississippi 246.39552 234.90121 227.99020 205.56439 192.39275 177.81860 159.63566 139.23874 71.04933
Riviere Petawawa 297.49319 281.57307 272.56700 243.21302 226.19822 204.94382 174.95789 155.88973 96.95898
Riviere Petite Nation 135.74763 129.01603 123.85775 109.91896 102.52234 94.70523 84.13372 75.59870 47.68063
Riviere Rideau 652.94365 607.97746 577.58451 494.67751 436.66629 364.82639 276.42475 231.05908 120.54403
Riviere Rouge 663.74795 641.99818 631.52646 581.00855 548.17706 507.33014 443.81107 389.84441 214.64020
Riviere South Nation 1453.79742 1269.14512 1220.78515 1058.08058 974.60152 865.68520 670.75702 523.05742 159.95954

Summary statistics at the basin level

As you will see in our summary statistic analyses, sometimes the observations entries show higher peaks than the simulations. Specially during summer. This time again, it’s Rapide-2.

Next, I compared the extent of the 170 000 prsim simulations light green font and also the mean green line. The observations forced into PRSIM (57 years) are in red. I plotted the maximum, the mean and the minimum.

I will show some of the 43 basins. As you can see, most of the means seem to be well simulated.

Jan 2000Mar 2000May 2000Jul 2000Sep 2000Nov 20000500100015002000250030003500
Average, High and Low PRSIM at BaskatongDaysStreamflow (cms)
Jan 2000Mar 2000May 2000Jul 2000Sep 2000Nov 2000050100150200250
Average, High and Low PRSIM at Rapide-2DaysStreamflow (cms)
Jan 2000Mar 2000May 2000Jul 2000Sep 2000Nov 20000100200300400500
Average, High and Low PRSIM at Rapide-7DaysStreamflow (cms)
Jan 2000Mar 2000May 2000Jul 2000Sep 2000Nov 2000020040060080010001200
Average, High and Low PRSIM at DozoisDaysStreamflow (cms)

Future work

Questions

Thank you!